But I'm thinking of incorporating a student feedback journal into that warm-up time once a week.

I'm imagining a journal where students self-reflect on their learning behaviors throughout the week and then I comment back with feedback- strategies to try, habits I notice, things to avoid, common mistakes, etc. At this point, I'm leaning strictly toward self-reflection, not mathematical work. The index cards will give me the feedback I need. I'd like this journal to give them the feedback they need.

I'm thinking I would do that on Mondays and that would give me the rest of the week and the weekend to respond to each student.

So on our first Monday back, I'm thinking about asking them to reflect on the final exam. I like the questions from crstn85's Test Correction's post:

How did you study for this test?
Did you feel prepared before you took the test?
Did you feel you were doing well while you were taking the test?
Are you happy with the grade you earned?

I'm imagining I will get responses like:
"You can't study for a math test."
"Why study when you let us use index cards?"
"My grade sucks."
"I thought I would do good until I got to #1."
"This test was nothing like what we do in class."

I'm imagining I will respond like this:
"I need to teach you how to study for a math test."
"Index cards are a reminder, but they can't remind you if you never learned in the first place. How could we use index cards better?"
"What could you do next time to improve your grade?"
"What made you feel confident before the test? What made you lose confidence?"
"If this doesn't look like what we did in class, what do we need to change?"

And so will begin a lovely give and take of communication. Right? Yeah, right.

I think the first time I will let them write freely. The second time, I hope to help them clean up their writing a bit. I plan to do this by answering the same questions they are answering, at the same time, from a teacher's perspective. Then the next week, I will put mine on the doc camera and have them compare their responses to mine. Hopefully, they will point out things like writing complete sentences, using capital letters and appropriate grammar, restating the question, not using text speak, etc. Then I can give feedback on their responses as well as to how their responses are written.

I really want the purpose of these journals to be twofold: 1. For them to self-reflect on their habits so that I can hold them accountable and eventually they can hold themselves accountable. 2. To give myself an easy opportunity to give attention and feedback to EVERY student.

Obviously, self-reflection is a big part of why we tweet and blog. Obviously, I don't need to lecture you on the merits of self-reflection, study habits, and writing. Eventually, I'd like this to lead to math portfolios. But first, I need to spend more time researching that idea, deciding what I want those to be, and ultimately, creating one myself. My fairy godteachers @druinok and @approx_normal helped me to realize that I need to go through the experience myself before putting my students through that experience. It needs to be meaningful and have purpose. I also have a tendency to rush in to things, give up too quickly, and try to take on the world all at once. See, self-reflection + teacher feedback = better behavior.

If you noticed, I did a lot of 'imagining' and 'thinking' in this post. And now here's your chance to bring me back to reality.

Comparing and contrasting is a higher level thinking skill important across the curriculum. We compare and contrast characters in a story, word choice in writing, equations in math (think < > =, not to mention word problems ), different hypothesis in science, how holidays are celebrated in different cultures, etc. That is probably why comparing and contrasting shows up multiple times in the Common Core Standards. Here are some ideas for comparing and contrasting in your class.

Venn Diagrams. In addition to using them on paper, you can make big ones on the floor with hula hoops and have kids use labeled index cards or Post Its to fill in the variables.

Analogies are great because you can use different criteria and then talk about which criteria was used. For example the analogy: Mountain: Hill : : River : Stream is defined by size while: December : Christmas : : February : Valentine's Day is defined by time. Here is a free Analogy Worksheet.

Similes and Metaphors Like Analogies, students can identify what the criteria is for the comparison. Similes may be easier for younger students because the words "like" and "as" pretty much tell you what the criteria is, while you often have to work a little harder with a metaphor.

Foldables can be used in so many ways for comparing and contrasting! Here are instructions on how to make some of the most common foldables.

Rating and Ranking There are so many ways to use this. Students can use numbers to rank brainstormed ideas. They can use a rating scale to evaluate their own work, peer presentations, the usefulness of a particular lesson etc.

Comparisons over Time Everyone loves to see improvement. Having students complete a variety of tasks at the start of the year and then doing the same ones at the end is a wonderful way to compare then and now. Do this on a smaller scale with a pretest and post test for any unit of study.

T Charts Simple, basic, effective and applicable to so many things. You can put a variable on each side of the chart (eg "Conductor" and "Insulator") or you could put the words "Same" and "Different" on each side and put a the things to be compared at the top (eg: "Mammals" and "Reptiles").

Written Essay No one should leave school without being able to write a solid, well-organized compare and contrast essay, complete with examples from life or literature. They will need these skills for the essay portion of the SAT.

I do these more for myself than anyone else, but here, I am quoting the most useful parts of this ASCD book (click links to read online for free). Basically, I'm editing out the boring. You're welcome.

I'm also just doing a couple of chapters at a time because it's kind of dry and I never know how much time I will have to read. So consider it a series if you like.

So the question becomes: If students have been taught the material and haven't learned or retained it, what can we as professionals do to change the scenario?

Writing [in this way] slows down and focuses my thinking; I am able to hear each word in my head and see it on paper. It is like a mindful meditation during which I shut out the rest of the world and am totally engaged in the process.

Another benefit of writing is that it allow the page to become a holding place for our thoughts until we can build upon them. We can revisit our written thoughts as often as needed and thus revise our thinking. Although I start with an overall plan when I write, I do not know where the ideas and words will take me until the process of writing drags them out of me- much as many artists do not know where a picture is going until the paint touches the canvas.

Mathematics is beginning to be viewed less as a series of arithmetic calculations than as "the science of order, patterns, structure, and logical relationships" (Devlin, 2000).

As Zinsser stresses in his book Writing to Learn (1989), it is important that all students be involved in the mathematics classroom. Twenty-five students cannot all speak at the same

time, but they can all write at the same time, and writing encourages them to become engaged in their learning.

Written explanations in mathematics are about what is being done and why it works. The type of thinking involved in justifying a strategy or explaining an answer is quite different from that needed to merely solve an equation. The process of writing about a mathematics problems will itself often lead to a solution.

Once students have done some initial writing about a problem, they can share their strategies in small groups. In attempting to solve the problem, the students will have additional opportunities for writing.

If students begin the problem on their own, they are starting from their own mathematical way of thinking. Bringing their written solutions to the small group helps students investigate mathematics more deeply.

Students need to untangle what is in their own minds first, get it on paper, and then share their thinking with others. (Love this statement with all my heart!) This ensures that there will be a range of responses to each question.

To quote Stigler and Hiebert (1999):

When this type of learning experience is used, the range of individual differences will be revealed. Individual differences are beneficial for the class because they produce a wide range of ideas and solution methods that provide the material for students' discussion and reflection. The variety of alternative methods allows students to compare them and construct connections among them. It is believed that all students benefit from the variety of ideas generated by their peers. (p. 94)

In order for mathematics writing to be effective, the following guidelines must be observed:

The problem must be appropriate for the students who are going to be writing about it.

The students must know how to use blocks, diagrams, pictures, or grids to work out their solutions before writing about them.

The students must have confidence in their ability to respond to the problem as individuals. They must think of themselves as successful mathematics learners.

The students must feel comfortable sharing their answers without fear of being ridiculed. This means that the teacher and other students have to accept all responses as worthy of discussion.

The problem must be discussed with the whole class, and all strategies must be reported.

Other writing-to-learn strategies include journal keeping, creating problems similar to the one being solved, and directed expository writing.

In other words, teachers should use writing to engage students in mathematics thinking at the outset of a lesson and continue asking them to put their thinking in writing throughout the lesson to refine their thinking.

As the NCTM (2000) notes,

...Allowing students to grapple with their ideas and develop their own informal means of expressing them can be an effective way to foster engagement and ownership. (p. 63)

By recording their thinking about mathematics problems, students help explain the solutions- and the process of arriving at a solutions helps to develop the solution. Writing clarifies what it is the problems are asking. In order to justify their solutions, student writers are forced to think through, and find the meaning in, their responses.

Student writing helps teachers determine the type of learning that is occurring, informs them as to whether or not the students understand the lesson objectives, and reveals the level of understanding behind the students' algorithmic computations.

"But another approach — since you used the word “enjoy” — is to simply consider math as an opportunity for puzzle-solving in interesting ways. After all, there is virtually NOTHING “personally relevant” in many of the games and pursuits people find so compelling, like, for example, Sudoku. Even chess. Or Angry Birds. Whether math is useful/relevant RIGHT NOW is a worthy and challenging goal."

"I too believe in the value of building on students’ experiences, but rather than look for experience in the form of mathematical content appearing in their everyday lives, I look for experience in the form of mathematical thought processes—such as classifying, identifying patterns, and generalizing—and, most important, a desire to solve problems and make sense of the world."

I then took to Twitter with my complaints and lonely fit of rage. No one's responses were satisfying my need for a 'real-life' answer and so I sullenly accepted their responses with a doubtful 'I guess'. And then...IN SWOOPS...the calming voice of reason, aka @jackieb. She questioned me on why I first chose to teach math.

The short answer is that everything else seemed boring. The long answer is that my best subject was English but I couldn't bear the idea of teaching grammar and listening to students stuttering through reading aloud for the remainder of my days. I suck at science and history. Art was fun but I didn't have much skill to back it up. So that left me with math. The more I thought about it, the more it made sense. I like organizing and ordering things, figuring out puzzles, observing patterns, solving problems, and in general, making things work better. Plus, math is interactive; I would always be doing something.

When I said this to Jackie (in <140 characters) she calmly responded with:

Those sound like great "likes" for your students to like too. They may never "use" Alg2, but they'll use problem solving. Can you try to develop that sense of wanting to try to figure things out in your students?

I can't always relate things to real life. In precalc I tell them that I don't know if they'll ever use this, but that I don't know what they'll be doing in 10 years. I then tell them I don't want them to not have choices open to them because they can't do math. Then we talk about the value of learning just for the sake of learning, the challenge of being able to solve tough problems,task perseverance, ... , then they get tired of me talking so much, so we get back to solving problems.

How can I expect my students to be better if I don't give them the tools to do it with? I am subconsciously (or consciously I suppose) saying, "You won't ever need these skills because I don't believe you can ever become an engineer, mathematician, programmer, etc." I'm doing the exact opposite of what I intend. Not that that's ever happened to you of course.

So now I am thinking...how can I lead my content, my class, my lessons around the fact that everyone loves a puzzle/pattern/mystery? How can I lead with what I enjoy so that my joy spills over into my students and their thinking and their actions?

Is there a pattern (very punny!) I can create so that our daily math experiences revolve around figuring out a pattern, solving a problem, mastering a puzzle?

Can I train students to think of life in terms of:

What do I know?

What pattern do I see?

What do I predict happens next?

How will changing the pattern affect the ending?

Can I change the pattern to create a different ending?

What patterns can I create to achieve the ending I want?

Hey, that kind of sounds like we're reading a story. Or avoiding bad relationships. Or being a better friend. Or breaking a bad habit.

And that sounds a lot more like real life than using systems of equations to decide which cell phone plan is better.

I do these more for myself than anyone else, but here, I am quoting the most useful parts of this ASCD book (click links to read online for free). Basically, I'm editing out the boring. You're welcome.

I'm also just doing a couple of chapters at a time because it's kind of dry and I never know how much time I will have to read. So consider it a series if you like.

*An ESL student thought of 'whole' numbers as 'hole' numbers, as in how many holes a number add. He thought 6 and 10 were odd numbers because they each only have one hole. He didn't know if 3 was even or odd because it could be considered as having two holes or two half holes which would make one whole hole. He knew the definition of even or odd but misunderstood 'whole'.

Younger students can be quit mystified by the fact that changing the orientation of a symbol- for example, an equal sign (=) from horizontal to vertical- can completely change its meaning.

Vocabulary can be confusing because the words mean different things in mathematics and nonmathematics contexts, because two diferent words sound the same, or because more than one word is used to describe the same concept.

Symbols may be confusing either because they look alike (e.g., the division ad square root symbols) or because different representations may be used to describe the same process.

Graphic representations may be confusing because of formatting variations or because the graphics are not consistently read in the same decision.

One strategy we arrived at is for teachers to model their thinking out loud as they read and figure out what a problem is asking them to do. Other strategies include dialoguing with students about any difficulties they may have in understanding a problem and asking different students to share their understanding.

James Bullock (1994) defines mathematics as a form of language invented by humans to discuss abstract concepts of numbers and space.

The meaning that readers draw will depend largely on their prior knowledge of the information and on the kinds of thinking they do after they read the text (Draper, 2002): Can they synthesize the information? Can they decide what information is important? Can they draw inferences from what they've read?

In English there are many small words, such as pronouns, prepositions, and conjunctions, that make a big difference in student understanding of mathematics problems. For example:

The words of and off cause a lot of confusion in solving percentage problems, as the percent of something is quite distinct from the percent off something.

The word a can mean “any” in mathematics. When asking students to “show that a number divisible by 6 is even,” we aren't asking for a specific example, but for the students to show that all numbers divisible by 6 have to be even.

When we take the area “of” a triangle, we mean what the students think of as “inside” the triangle.

The square (second power) “of” the hypotenuse gives the same numerical value as the area of the square that can be constructed “on” the hypotenuse.

In her book Yellow Brick Roads (2003), Janet Allen suggests that teachers need to ask themselves the following critical questions about a text:

What is the major concept?

How can I help students connect this concept to their lives?

Are there key concepts or specialized vocabulary that needs to be introduced because students could not get meaning from the context?

How could we use the pictures, charts, and graphs to predict or anticipate content?

What supplemental materials do I need to provide to support reading?

If we are really trying to help students read and understand for themselves, we must ask them questions instead of explicitly telling them what the text means: “What information do you have that might help you answer this question?” “Does the fact that this is a ‘follow-up’ help us to decipher the question?”

As the reading progresses, the teacher should ask process questions that she wants the students to ask themselves in the future. They may be asked to predict what the reading will be about simply by reading the title of the piece (if there is one, such as a graph or story problem). Next the students should make two columns on a piece of paper, one headed “What I Predict” and the other headed “What I Know.” Once the students have silently read each section of the piece, they should fill out each column accordingly. At this point, the teacher should ask students questions such as the following:

What would you be doing in that situation?

Does this make sense?

What does the picture/graph/chart tell you?

How does the title connect to what we're reading?

Why are these words in capital letters?

Why is there extra white space here?

What does that word mean in this context?

Figure 2.4 shows a simple example of a possible guided reading for a lesson from an algebra text. The text would be unveiled one paragraph (or equation) at a time rather than given to the students as one continuous passage.

Figure 2.4. Guided Reading Example

TEXT

POSSIBLE QUESTIONS

Solving Systems Using Substitution

1. What does the title tell you?

Problem

From a car wash, a service club made $109 that was divided between the Girl Scouts and the Boy Scouts. There were twice as many girls as boys, so the decision was made to give the girls twice as much money. How much did each group receive?

2. Before you read further, how would you translate this story problem into equations?

Solution

Translate each condition into an equation.

Suppose the Boy Scouts receive B dollars and the Girl Scouts receive G dollars. We number the equations in the system for reference.

3. What do they mean here by “condition”?

The sum of the amounts is $109.

(1) B + G = 109

Girls get twice as much as boys.

(2) G = 2B

4. Did you come up with two equations in answer to question 2 above? Are the equations here the same as yours? If not, how are they different? Can you see a way to substitute?

Since G = 2B in equation (2), you can substitute 2B for G in equation (1).

B + 2B = 109

3B = 109

B = 36 1/3

5. How did they arrive at this equation?

6. Do you see how it follows?

7. Does it make sense? How did they get this?

To find G, substitute 36 1/3 for B in either equation. We use equation (2).

8. Do this, then we'll read the next part.

G = 2B

= 2 × 36 1/3

= 72 2/3

So the solution is (B, G) = (36 1/3, 72 2/3).

The Boy Scouts will receive $36.33, and the Girl Scouts will get $72.67.

9. Did you get the same result?

Check

Are both conditions satisfied?

10. What conditions do they mean here?

Will the groups receive a total of $109?

Yes, $36.33 + $72.67 = $109. Will the boys get twice as much as the girls? Yes, it is as close as possible.

11. How would you show this?

Where did they get this equation?

Note: Text in the left column above is adapted from University of Chicago School Mathematics Project: Algebra (p. 536), by J. McConnell et al., 1990, Glenview, IL: Scott Foresman.

Students are helped not by having their reading and interpreting done for them, but rather by being asked questions when they don't understand the text. The goal is for students to internalize these questions and use them on their own.

12.24.2011

I start out by teaching how to pull out the GCF, how to factor by grouping, then how to factor x^2 + bx + c using the diamond or the x-factor method. Those kind of have to be taught before this method. But it works.

I used the same problems she did so that you can compare the different methods.

The original problem

Multiply the first and last numbers. This answer, -12, is the top of the x.

The bottom of the x is the coefficient of x, in this case -1.

The sides of the x are two numbers that multiply to equal -12 and add to equal -1.

The students have a LOT of practice with the x-factor so they find that its -4 and 3.

Now they rewrite the problem, replacing the -x with a -4x + 3x.

Draw in our parentheses and now we have factoring by grouping, which students are also very familiar with.

This is a review of my semester so far to help me focus on things I need to change and for me to evaluate our progress by the end of the year. So if you don't want to be bored to tears, go ahead and click around somewhere else.

Achievement Period- The best thing we've started doing is going down to the elementary once a week and working with the students one-on-one during their guided reading time. The teachers adore it, the kids get individual attention, I don't have to do anything, and my students feel like rock stars. I think it unifies them and boosts their confidence in their own ability. We were doing Silent Reading on Tuesdays which fell to the wayside but I will definitely be bringing that back. I need to devote one day to Career Cruising, even if I do think it's useless. That takes up three days a week. I'm planning on doing that on Fridays and having students print out a current event off the Internet so we can discuss that on Monday. Plus we talk about our weekends on Mondays so that will pretty much take up the whole period. That leaves me with Wednesday. I need to find some good character ed activities. Otherwise it will end up being study hall which means chaos.

ACT Test Prep- I started the year with the lowest of the lows and it was miserable. They desperately needed differentiated instruction that I just could not get. My management skills, as always, were terrible. The class is supposed to be a refresher but you can't refresh what they've never learned. Then we rotated and I got the high of the highs. It was lovely. I haven't taught top students in forever. They care about their scores, they try, they explain, they work together, they listen, they know things. They still don't bring pencils and they too roll their eyes and sigh heavily but hey, they're teenagers. It's like a natural reaction. Our routine is to practice problems, the next day take a short test, the third day go over test results and commonly missed problems, the next day is Silent Reading, and the last day is a study hall. My instructional coach had all the materials made from last year so I basically make copies and answer key and then let them loose. I have one more week with them and then we rotate to the middle or what we call bubble kids. The plan was that I would have them closest to the actual test date because math is our downfall and maybe we could push a few into the meets category. I will hate to lose these top students but anything is better than the lows. I felt terrible every day because I knew I was not doing them any justice whatsoever. Nobody needs a daily reminder of their failure.

Algebra II- My favorite class of all! I've gotten some really good resources from another teacher but having only 5 students takes the cake, I love, love, love it. The class runs itself and they do all of the work. I make the bell ringer with five problems and each student is responsible for doing one on the board and explaining to the class. We do a lot of board work or just them working together and I roll around in my rolly chair and help. They have totally blown me away with their reasoning and critical thinking and plus, they are really entertaining.

Plan- The last few weeks of the semester I started getting to school about 30 minutes earlier and getting all of my copies made for the day and my classroom setup. It started me off in a much better mood and also freed up my plan period to accomplish other things. I'm super proud of that.

Algebra I- I think Algebra II has stolen my love away from Algebra I. I think the class is just a weird mix and since they are freshman, I still think they haven't really got used to me. It's kind of a weird, stiff environment. My other students have had me now for two or three years in a row and so they are waaaay different around me. My pacing guide has really helped this year. Last year I got totally bogged down in linear equations for months and this year, I didn't. I'm proud of that. About half of the class stays with me, and the other half just...show up at random moments. lol I have an extra moody girl, a sneaky girl, a girl that works at a snail's pace, and a boy who thinks its cool to not try and fail. Those are the ones that I'm never sure what's going on in their minds. I have three who are really solid and basically keep the class going. It's a class of 10 which is a good number but...it's just not nearly as fun as it was. I don't even know what to say about it.

Algebra II- My other Algebra II class of 4 students. They aren't academically where my third hour class is and I have some problems with attendance, but the class is run the same way. It's great because these four students easily slipped through the cracks in previous years and now they cannot escape my individual attention. Cackle, cackle.

Geometry- The bane of my existence. It's strange because any thing I read or hear about, when I think about implementing it, it's in this class. My instructional coach bet me that this would end up being my favorite class since it's my biggest, 25. She was wrong. It's definitely been the one that's made me grow and stretch the most but I still detest it. My management skills are to blame once again. The thing that's worked the best, which doesn't mean it has worked, is giving them another homework problem every time they get too loud. I don't like punishing the whole class like that but then the quiet students are more likely to shush everyone. I have the most success when I play our review pong game. They love it and they do work together. They get a little loud but nothing compared to how they act during regular class. I moved them into pairs and I think that has helped because it creates much more space in the class but students still have someone they can talk to. I've gotten to teacher-centered again and need to start doing more student-centered activities. I also need to quit being a baby and just write people up but I just doubt that's going to happen.

Geometry Lab- This class is a waste of time. No one can tell me what I'm supposed to be doing and there is no curriculum. Basically, it is a class of sophomore Geometry students who did not meet on their Explore tests as Freshman. So we call it Geo Lab but students are supposed to be doing something to increase their test scores. Except nobody can tell me what that is. What I've started most recently is breaking them into groups of three. One group works with me on whiteboards learning a new skill. A second group works independently on their bids as part of their Real World Math projects. A third group works on the computers on ALEKS, which they absolutely hate. I'm thinking of using Khan Academy to replace ALEKS but I just detest those darn videos so much. I don't think he should stutter and I just don't think he explains it in the best way. But unless I decide to make my own (which I will eventually, just probably not this year) I guess I will have to suck it up and deal with it.

Extracurriculars- We did Homecoming in December this year so it will be really nice to not have to worry about that in January. Our boys basketball team is awesome this year so I am really enjoying going to their games. I've been presenting almost every month at our school improvement days about technology so I am loving that. It has opened the doors for me to talk to and work with other teachers and help send resources their way. I have spent the last couple years intimidated by others because so many teachers were my teachers. I never wanted to be the new teacher who acted better than everyone and like they knew everything so I really took a backseat. But now I am coming out of my shell! I just love more opportunities to teach! I've also been making our monthly agendas so now they are pretty and that makes my heart happy. We've done peer observations which have been really interesting and I love to have other teachers come and watch me. Our cohort is taking a teaching methods course right now in our graduate program. I have not been impressed with our classes so far. I suppose its because I read so much and blog and twitter but....I haven't learned anything yet. I've already known everything we've talked about and actually done most of it in my classroom. I also feel like there is major grade inflation here. Some teachers seemingly give A's to everyone which doesn't inspire me to try very hard. The only class that was new for me was on observation techniques, but I don't see getting to use them unless I actually become a coach or something. I still need to videotape myself and try the techniques. I officially am not in survival mode any longer. I am no longer panicked and feeling clueless. The amount of preps is tough but I haven't died yet. I'm feeling pretty solid. I'm done with my evaluations for the year and they went well so that's a relief. I noticed that I've migrated back to more teacher-centered and so that's a goal to work on this semester, along with my many ponderings. Also, I stood up for myself in a situation where I felt I was being treated unfairly. And that made me happy.

In a lot of things I've been reading recently, the topics of high expectations and self-fulfilling prophecy have shown up a lot. It's really had me thinking. What are my expectations for my students? Honestly...I don't think I've communicated any expectations at all. Except maybe to bring a pencil every day.

How do we express high expectations? How do we express expectations at all? What expectations have I expressed without knowing it? When I think about it, I imagine a grandiose speech at the beginning of the year where a teacher says what they expect. The end. How do you go about raising the bar and holding them accountable to higher standards? How do you hold them to it?

I had to write about this for my midterm in my graduate teaching methods class. First I had to tell of a personal account with a teacher and self-fulfilling prophecy. It was the hardest question on the entire test for me. I couldn't think of one single example, good or bad. I couldn't remember a teacher every saying anything that affected me that way. Then we had to write three action steps for raising expectations in our own classroom. I had to google it because I sure didn't know how! This is what I came up with:

One action step I could take to raise my expectations would be to implement the participation points contract mentioned in question number six. This would be a great way to clearly define my expectations for student behavior in my classroom. By having students read, check mark, and sign, they are agreeing to a higher level of behavior.

A second action step I could take would be modeling. I am thinking of implementing math portfolios in my classroom next year. What that means is that a student would be responsible for writing a skill description, creating an example and working it out, and explaining the problem solving process for the essential skills in any given unit. I would have to model for students an excellent, average, and unsatisfactory example so that students know my expectations are higher than just scribbling down a sentence.

My third action step would be to hold students accountable by consistently providing detailed feedback. Whether on homework, tests, classroom participation, or on portfolio assignments, by giving students detailed feedback on their progress, I am letting them know where they are and where I expect them to be. I’m also communicating to them that they cannot just slip by unnoticed and that they are expected to improve. Along with that, I am providing direct instruction to support and assist them with improving.

Am I totally off the mark here? The main thing I found during my googling followed along the themes of modeling. If I expect more out of them, then I have to clearly model what I expect. But clearly modeling expectations doesn't necessarily mean they are high expectations. I guess what I'm truly asking is, what are high expectations? What should I expect out of my students? And then, how do I express that?

I suppose modeling behaviors, exemplar assignments, and using rubrics to grade are ways of clearly defining what is expected. But how do you hold them to it? What do you do if they are not performing according to your expectations? I imagine a stern face, arms crossed, deep voice: "I expect better out of you." But that can't be it. It has to be more than just talk, right? Right?

How can I have great expectations when I don't know what great is or how to express it?

Student Feedback Notebook- A year-long dialogue between me and each student in a special notebook. Could: address academic, behavior, personal concerns, document progress, suggestions for improvement, highlight misconceptions, maintain meaningful relationships between me and each student, or just be really cool.

12.23.2011

Now I know that these are out of the ordinary teachers. The books made me laugh, cry, and get angry. Parts of them inspired me, parts of them made me want to quit. But what bothered me the most was...I couldn't relate.

I loved reading about how Erin Gruwell used pop culture to engage students in reading and writing. I loved how Ron Clark took his students on life changing field trips that related to what they were studying in history. But how does this apply to teaching math?

I can never think of ways to incorporate new ideas into what I teach. I can read something on the Internet, find a new iPad app, hear something at a conference, and immediately think of how it would work beautifully in English or Social Studies. I never know how to make things work for math.

I don't know how to relate math to real life. It doesn't relate. They will never use this stuff in real life. I sure don't. How will learning systems of equations help them deal with their problems at home? How will graphing parabolas help them avoid drama? How will using the distance formula help them face their fears and overcome obstacles and become amazing people? How can math be life changing?

I know I sound like one of my own whiny students, but I can't help it. These are emotions that I face time and again. I am not inspired by math, why should they be? Am I teaching the wrong subject?

How is it that I put in all this time and feel like I am killing myself and yet still only accomplishing a fraction of what other teachers are doing? We can't even use experience as an excuse. Erin Gruwell started doing crazy things even in her student teaching.

I'm not having a pity party or saying I suck. I'm saying that mentally, I cannot wrap my head around bringing math to life, relating it to the world, planning field trips around math, or making it inspiring.

I don't know how to be that person.

That frustrates me because I feel like I can't learn. And not being able to learn just upsets me to the very core of my being. I am a professional learner! I may suck at things but I can always learn how to be better. And now, I can't.

12.22.2011

I haven't blogged in so long I've almost forgotten how. I had all kinds of ideas I wanted to blog and no time to do it in- now the situation is reversed. I'm going to blog my most recent calamity in hopes that that will jog my memory...

I wrote really good final exams.

I worked really hard and am really proud of what I accomplished.

Then the students took them.

Uh-oh.

In the past two years, I wrote terrible finals. Things we never really talked about, missing graphs and diagrams, questions with no answers, etc. It was bad. I cried.

This year, they cried. Okay, only one actually cried.

I created the tests. Then I broke the material up into three different days of review in order to cover everything. We did worksheets, whole class reviews, group game reviews, working one problem at a time, and so on. After each concept we've learned, we stop and write an index card on how to do it and an example problem. The students were allowed to use these index cards on the final.

Each test was 35 questions. 30 multiple choice, 5 open-ended, and all of them required thinking. It took the majority of the students the entire hour and twenty minutes to finish. It was hard and they told me about it. But only one person said they felt like it was things we had never done before. That's a huge improvement for me personally. The grades were not very good. About half failed. Out of all of my classes I had one A. One. Wow. I think I surprised even myself. I felt compassion for them but not guilt like in previous years.

But in a lot of cases, I felt like the grade truly represented their knowledge And in some it clearly didn't.

I honestly feel like the content of the tests was within their reach. They're just not used to stretchig.

This single event has taught me the importance of backward design more than everything I have read, heard, and discussed with others. I'm all excited to plan my unit tests ahead of time during the next semester. I know I should have done this from the beginning so I don't need a lecture on that.

My dilemma is, what do I do with the students' grades? Do I let them stand in hopes that students will take things more seriously and try harder? Do I cushion them because my unit tests didn't line up with the final exam and that's my fault? Do I give them a chance to make corrections when it is supposed to be a summary of everything they've learned? Do I just get over feeling bad when it's only the first semester and I let them use index cards as well? Will I get in trouble when my principal sees such terrible grades?

I need help from all you final exam fairies.

P.S. I started teaching things in December that I was teaching last year in February. I beat myself by two months. That is the power of a pacing guide people!